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A Benchmark Approach to Filtering in Finance

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  • Eckhard Platen
  • Wolfgang Runggaldier

Abstract

The paper proposes the use of the growth optimal portfolio for pricing and hedging in incomplete markets when there are unobserved factors that have to be filtered. The proposed filtering framework is applicable also in cases when there does not exist an equivalent risk neutral martingale measure. The reduction of the variance of derivative prices for increasing degrees of available information is measured. Copyright Springer Science + Business Media, Inc. 2004

Suggested Citation

  • Eckhard Platen & Wolfgang Runggaldier, 2004. "A Benchmark Approach to Filtering in Finance," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 79-105, March.
    • Handle: RePEc:kap:apfinm:v:11:y:2004:i:1:p:79-105
    DOI: 10.1007/s10690-005-4301-4
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    1. Wolfgang Breymann & Leah Kelly & Eckhard Platen, 2005. "Intraday Empirical Analysis and Modeling of Diversified World Stock Indices," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(1), pages 1-28, March.
    2. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187, July.
    3. Robert J. Elliott & John van der Hoek, 1997. "An application of hidden Markov models to asset allocation problems (*)," Finance and Stochastics, Springer, vol. 1(3), pages 229-238.
    4. Fischer Paul & Platen Eckhard, 1999. "Applications of the balanced method to stochastic differential equations in filtering," Monte Carlo Methods and Applications, De Gruyter, vol. 5(1), pages 19-38, December.
    5. I. Bajeux-Besnainou & R. Portait, 1997. "The numeraire portfolio: a new perspective on financial theory," The European Journal of Finance, Taylor & Francis Journals, vol. 3(4), pages 291-309.
    6. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    7. Leah Kelly, 2004. "Inference and Intraday Analysis of Diversified World Stock Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2004.
    8. Carl Chiarella & Sara Pasquali & Wolfgang J. Runggaldier, 2001. "On Filtering in Markovian Term Structure Models," World Scientific Book Chapters, in: Jiongmin Yong (ed.), Recent Developments In Mathematical Finance, chapter 12, pages 139-150, World Scientific Publishing Co. Pte. Ltd..
    9. Ram Bhar & Carl Chiarella & Wolfgang Runggaldier, 2001. "Filtering Equity Risk Premia From Derivative Prices," Research Paper Series 69, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. David Heath & Eckhard Platen, 2001. "Pricing and Hedging of Index Derivatives under an Alternative Asset Price Model with Endogenous Stochastic Volatility," World Scientific Book Chapters, in: Jiongmin Yong (ed.), Recent Developments In Mathematical Finance, chapter 10, pages 117-126, World Scientific Publishing Co. Pte. Ltd..
    11. Rüdiger Frey & Wolfgang J. Runggaldier, 1999. "Risk-minimizing hedging strategies under restricted information: The case of stochastic volatility models observable only at discrete random times," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 339-350, October.
    12. David Heath & Eckhard Platen, 2002. "Perfect Hedging Of Index Derivatives Under A Minimal Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(07), pages 757-774.
    13. Ram Bhar & Carl Chiarella & Wolfgang Runggaldier, 2001. "Estimation in Models of the Instantaneous Short Term Interest Rate By Use of a Dynamic Bayesian Algorithm," Research Paper Series 68, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Eckhard Platen & Gerhard Stahl, 2003. "A Structure for General and Specific Market Risk," Computational Statistics, Springer, vol. 18(3), pages 355-373, September.
    15. Carl Chiarella & Sara Pasquali & Wolfgang Runggaldier, 2001. "On Filtering in Markovian Term Structure Models (An Approximation Approach)," Research Paper Series 65, Quantitative Finance Research Centre, University of Technology, Sydney.
    16. Rüdiger Frey & Wolfgang J. Runggaldier, 2001. "A Nonlinear Filtering Approach To Volatility Estimation With A View Towards High Frequency Data," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 199-210.
    17. Eckhard Platen, 2002. "Benchmark Model with Intensity Based Jumps," Research Paper Series 81, Quantitative Finance Research Centre, University of Technology, Sydney.
    18. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
    19. Ralf Korn & Manfred Schäl, 1999. "On value preserving and growth optimal portfolios," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 189-218, October.
    20. Andrea Gombani & Wolfgang J. Runggaldier, 2001. "A Filtering Approach To Pricing In Multifactor Term Structure Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 303-320.
    21. Bhar Ramaprasad & Chiarella Carl & Runggaldier Wolfgang J., 2004. "Inferring the Forward Looking Equity Risk Premium from Derivative Prices," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(1), pages 1-26, March.
    22. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    23. Robert Elliott & Eckhard Platen, 1999. "Hidden Markov Chain Filtering for Generalised Bessel Processes," Research Paper Series 23, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Citations

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    Cited by:

    1. I. Venkat Appal Raju & N. Selvaraju, 2012. "Growth Optimal Portfolio for unobservable Markov-modulated markets," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(1), pages 31-40.
    2. Eckhard Platen & Wolfgang Runggaldier, 2007. "A Benchmark Approach to Portfolio Optimization under Partial Information," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(1), pages 25-43, March.
    3. Ke Du & Eckhard Platen, 2011. "Three-Benchmarked Risk Minimization for Jump Diffusion Markets," Research Paper Series 296, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Claudio Fontana & Wolfgang J. Runggaldier, 2012. "Diffusion-based models for financial markets without martingale measures," Papers 1209.4449, arXiv.org, revised Feb 2013.
    5. Alexandre Ziegler, 2007. "Why Does Implied Risk Aversion Smile?," The Review of Financial Studies, Society for Financial Studies, vol. 20(3), pages 859-904.
    6. Mark H.A. Davis & Sébastien Lleo, 2021. "Risk‐sensitive benchmarked asset management with expert forecasts," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1162-1189, October.
    7. Alexandre Ziegler, 2002. "Why does Implied Risk Aversion Smile?," FAME Research Paper Series rp47, International Center for Financial Asset Management and Engineering.
    8. Ionela Munteanu, 2020. "Financial Reporting Quality and Operational Efficiency in the Coastal Region of Romania," Ovidius University Annals, Economic Sciences Series, Ovidius University of Constantza, Faculty of Economic Sciences, vol. 0(2), pages 978-984, December.
    9. S'ebastien Lleo & Wolfgang J. Runggaldier, 2023. "On the Separation of Estimation and Control in Risk-Sensitive Investment Problems under Incomplete Observation," Papers 2304.08910, arXiv.org, revised Nov 2023.

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    More about this item

    Keywords

    financial modeling; stochastic filtering; benchmark approach; growth optimal portfolio; fair pricing under partial information;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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